This invention relates to analog modem technology. Specifically, it proposes a new precoding scheme to achieve higher rates in the analog modem to digital modem direction.
FIG. 8 shows the basic elements of an end-to-end transmission within the Public Switched Telephone Network (hereinafter xe2x80x9cPSTNxe2x80x9d). The PSTN shown includes first and second Users, first and second Central Offices, and a Switched Digital Network. Analog Subscriber Loops connect the Users to their respective Central Offices, and the Switched Digital Network connects the Central Offices together. The Analog Subscriber Loops are conventional twisted pairs that transport analog signals from the User Equipment to the associated local Central Office. At the Central Office, the analog signals are converted to 64 kbps DS0 digital data streams by a channel unit filter and codec, which together implement a bandlimiting filter followed by subsequent analog to digital conversion using a nonlinear encoding rule. The resulting DS0 streams are transported to their respective destination Central Office via the Switched Digital Network.
At the Central Office 1, User""s 1 loop signal is first bandlimited. The bandlimited analog signal is then sampled at a rate of 8 ksamples/second, and then converted into an 8-bit digital representation using a nonlinear mapping rule referred to as PCM encoding. This encoding is approximately logarithmic, and its purpose is to permit relatively large dynamic range voice signals to be represented with only 8 bits per sample.
Users 1 and 2 may use a conventional modem, as shown in FIG. 9, to transmit digital data over the configuration of FIG. 8. The conventional modem encodes the user""s digital data into a symbol sequence. The symbol sequence is then represented as an appropriately bandlimited analog signal which can be transmitted over the approximately 3.5-4 kHz bandwidth available on the end-to-end connection. The exemplary modem of FIG. 9 includes a Digital to Analog converter (i.e. D/A),) an Analog to Digital converter (i.e. A/D), and a hybrid. The A/D and the D/A perform PCM encoding and decoding, respectively
PCM baseband modulation in the upstream direction, i.e. from User 1 to the Central Office, presents special equalization problems. For instance, one potential application for PCM baseband modulation in the upstream direction is in conjunction with xe2x80x9c56kxe2x80x9d modems. However, xe2x80x9c56kxe2x80x9d modems have a zero in the frequency band of interest. The zero at zero frequency comes from the transformer coupling of the analog subscriber loop to the central office equipment. Therefore, telephone lines do not pass DC signals. Low frequencies near DC are also attenuated significantly as to rule out linear equalization of this channel. Moreover, it is not possible to avoid the zero at DC for 56k modems using pass-band modulation as in the case of earlier V.34 modems because the central site modem is limited to using the sampling rate and quantization levels of the PCM codec at the central office.
One possible way to equalize this channel is to use a linear equalizer to reduce the channel response to a simpler xe2x80x9cpartialxe2x80x9d response that still possesses the zero in the channel but can be dealt with using a non-linear technique such as maximum likelihood sequence (MLSE) decoding or decision feedback equalization (DFE). This however is only possible in the direction of digital modem to analog modem, also referred as the downstream direction. The reason this approach or any linear equalization scheme does not work in the upstream direction is that only PCM codec levels themselves can pass through the PCM codec unscathed. Any filtered version of a sequence of PCM levels will be a linear combination of these levels and in general not be a PCM level itself. When such intermediate levels are quantized by the PCM codec, quantization noise is introduced into the signal erasing any advantage over V.34 techniques.
Accordingly, there exists a need for a system capable of equalizing transmissions from an analog modem.
The inventor has recognized that one way to overcome the difficulties noted in the background of the invention is to use preceding in the transmitter, in place of MLSE or DFE in the receiver, and to use decoding in the receiver. In this way PCM levels can be used as the symbol constellation. The combination of the precoder and a linear equalizer will eliminate the inter-symbol interference (ISI) introduced by the channel. In this manner signals arriving at the PCM codec will be free of ISI and no quantization noise will be introduced.
The simplest manner of implementing preceding is to implement a feedback filter that equalizes the partial response. This however is not practical in the case where the channel and hence the partial response possesses a zero in the band of interest. The reason is that since the feedback filter equalizes the partial response, it has a very large gain at the frequency where the partial response has a zero. Components in the transmitted signal that correspond to this frequency will be greatly amplified leading to an unstable feedback loop.
Tomlinson Harashima Precoding (xe2x80x9cTHPxe2x80x9d) has emerged as an attractive solution for equalization in the presence of severe channel attenuation in the frequency band of interest; See M. Tomlinson xe2x80x9cNew Automatic Equalizer Employing Modulo Arithmeticxe2x80x9d Electronics Letters Vol. 7, pp. 138-139, March 1971, the contents of which are incorporated herein by reference; and See H. Harashima and H. Miyakawa xe2x80x9cMatched-Transmission Technique for Channels with Intersymbol Interferencexe2x80x9d IEEE Trans. Commun. Vol. COM-20, pp. 774-80, August 1972, the contents of which are incorporated herein by reference. THP is equivalent to Decision Feedback Equalization (DFE) in the receiver without the potential problem of error propagation.
The clever solution to the problem of very large gain at frequencies where the partial response has a zero is provided in the THP as follows. Whenever the output of the feedback loop passes a present threshold, the transmitted signal is subjected to a modulo operation which brings it back within range. This removes the instability in the feedback loop of the transmitter. The receiver must also account for the modulo operation in the transmitter. The receiver, since the modulo operation can be expressed as the subtraction of a constant, will compensate by adding the constant to the received signal. The receiver knows when to perform this compensation because whenever the transmitter subtracts the constant to bring the transmitted value to within range, the received value in the receiver will be out of range. When the receiver compensates the received signal by adding the constant, the received signal is brought back within range
However, the standard THP scheme is not effective for PCM encoding in the upstream direction because the receiver can not implement the modulo compensation without introducing quantization noise. If the transmitter implements the standard THP modulo operation, then the received signal will arrive at the PCM codec with a value that corresponds to a PCM value shifted by a constant. In general it is not possible to find a set of PCM values and a constant such that each PCM value, when shifted by a constant is another PCM value. Thus THP scheme as previously defined is not effective for PCM modems.
This invention modifies the standard THP algorithm to adapt it for use in PCM modems. Instead of an arithmetic modulo operation that is implemented in the transmitter, the invention utilizes a Discrete Modulo Operation to map a constellation level outside the basic constellation of levels onto a constellation level inside the basic constellation of levels. In accordance with the invention, a precoder map the input signals in a plurality of distinct ranges onto a basic level, in the basic constellation of levels, according to different arithmetic rules. This operation limits the amplitude of the transmitted signals, hence removing the instability of the feedback loop, while ensuring that received signals at the PCM codec are always within the PCM level set free of quantization noise. Similarly, a decoder is defined for the receiver to map received PCM values correctly into the symbol constellation.
In one aspect of the invention, the decoder of the receiving modem generates a decoded signal from a received signal. The decoder includes a mapper that generates the decoded signal by mapping received signals in a plurality of distinct ranges onto a basic level. The mapping of the plurality of distinct ranges onto the basic levels follows different arithmetic rules for at least two of the distinct ranges.
In another aspect, the invention comprises a decoding method of mapping a received signal contained in a first distinct range onto a basic level according to a first arithmetic rule, and mapping a received signal contained in a second distinct range onto the basic level according to a second arithmetic rule.